Solving a trigonometry equation --- SMO 2013

#olympiad #math #algebra #jee #trigonometry #geometry #gmat #mathstrick #olympiad2022

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[drozfarnyline]

hi! after getting the value of sin2θ=(12/13)
you calculated the value of cos2θ by pythagorean identity
Sin^2(x)+cos^2(x)=1
But can you tell me why didnt you give a plus minus (±)
I mean shouldn't the value of cos2θ=±√ (1-(144/169))
Thanks in advance

[samiralkayed]

Why you choose only the positive value of cos(2x)? why you don't take -5/13

[sachs]

I've got ±⅚, than I thought I'd missed a reason to reject the negative value, because you gave only one answer. But Wolframalpha helped me find that θ = 2arctan((-2-√13)/3) proves the negative solution is also valid.